Everyone buying a pizza at JR’s pizzeria gets a card that conceals either a J or

Question

Everyone buying a pizza at JR’s pizzeria gets a card that conceals either a J or an R. When the wax covering is rubbed off, the chance is 90% that a J will appear. Different cards can be treated as having independent letters. Once a person has both a J and R, she is entitled to a free pizza. Note that, because the same letter can come up on several successive purchases, that rule is not equivalent to one free pizza per two paid ones. If Pamela starts patronizing the pizzeria, find the probability that: (a) She receives an R on her first purchase. (b) Her first two purchases yield a J and R, in that order. (c) She is eligible for a free pizza after her first two purchases. (d) It takes her exactly three purchases to earn a free pizza.

Explanation / Answer

ind the probability that: (a) She receives an R on her first purchase.

Probability = 0.10

(b) Her first two purchases yield a J and R, in that order.

Probability = 0.90 * 0.10 = 0.09

(c) She is eligible for a free pizza after her first two purchases.

Probability = 0.90 * 0.10 + 0.10*0.90 = 0.18

(d) It takes her exactly three purchases to earn a free pizza.

Probability = 0.18^3 = 0.005832

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